Details

sample37.0ms

Algorithm

intervals

Results

8.0ms	40×	body	2560	valid
7.0ms	187×	body	80	valid
4.0ms	23×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	83	16
4	102	16
5	110	16
done	110	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

33.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
44.0ms	(- (* b b) (* (* 3.0 a) c))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify480.0ms

Counts

102 → 102

Iterations

Useful iterations: done (478.0ms)

Iter	Nodes	Cost
0	167	1697
1	444	1586
2	1573	1363
done	5000	1353

prune272.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0b	(/ (/ (+ (* 3.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.8b	(/ (+ (* 3.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

16.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
51.0ms	(/ (/ (+ (* 3.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
35.0ms	(/ (+ (* 3.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
139.0ms	(/ (/ (+ (* 3.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
169.0ms	(/ (+ (* 3.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4s

Counts

244 → 244

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	338	10795
1	848	8234
2	3179	6673
done	5000	6650

prune532.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
14×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-cbrt-cube`
8×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `div-exp` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `times-frac` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `flip3--` `pow-flip` `sqrt-div` `1-exp` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `neg-log` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv` `inv-pow`

Counts

4 → 90

Calls

4 calls:

4.0ms	(/ 1 (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (* 3.0 a))
47.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify522.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	152	1159
1	384	1039
2	1383	925
done	5001	925

prune245.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 3.0 a) c)
0.8b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
46.0ms	(- (* b b) (* (* 3.0 a) c))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify506.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	135	1109
1	351	1006
2	1323	900
done	5001	900

prune218.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

regimes317.0ms

Accuracy

85.5% (3.9b remaining)

Error of 9.2b against oracle of 5.3b and baseline of 32.3b

bsearch157.0ms

Steps

Iters	Range		Point
8	1.9086145032856143e-23	7.928945926733413e-19	1.772190746664465e-19
9	1.2164171611905196e-216	4.13282170633036e-209	4.515321176082739e-212
7	-2.3888623512096697e+55	-3.7205165428256016e+53	-2.245039883241749e+55

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	74
1	51	74
done	51	74

end0.0ms

sample1.1s

Algorithm

intervals

Results

235.0ms	1075×	body	2560	valid
212.0ms	5843×	body	80	valid
162.0ms	906×	body	1280	valid
99.0ms	2890×	body	80	nan
63.0ms	453×	body	640	valid
26.0ms	101×	body	5120	valid
24.0ms	234×	body	320	valid
8.0ms	119×	body	160	valid